(CBS) After a series of meetings this week between President Obama and members of Congress, lawmakers have yet to reach a deal to end the government shutdown or raise the debt limit. They did, however, agree to keep talking about it.

"We're obviously in a better place than we were a few days ago in terms of the constructive approach we've seen," White House spokesman Jay Carney told reporters Friday.

Mr. Obama and House Speaker John Boehner, R-Ohio, spoke on the phone Friday afternoon, and Carney said "the two of them agreed all sides need to keep talking on the issues here that ... have lead to the shutdown of the government and the situation that has put us on the precipice of potential default."

Mr. Obama met with Senate Republicans at the White House Friday, a day after meeting with House Republicans and hearing their offer to pass a no-strings-attached bill to raise the debt limit for just another six weeks. The president pushed back against the plan, asking Republicans to end the shutdown as part of the deal. He also reiterated that ongoing budget negotiations could and would cover all potential GOP hot button subjects -- but only after the default and shutdown issues were resolved.

After continued talks overnight between the White House and congressional offices, House Republicans sent the White House a modified deal for a short-term debt limit hike that sets up a framework for negotiations on a bigger budget deal.

Carney said Friday that Mr. Obama "appreciates the constructive nature of the conversation and the proposal that House Republicans put forward." However, he added, "He has some concerns with it."

"The president's position that we the United States should not, and the American people cannot, pay a ransom in exchange for Congress doing its job remains as true today as it has throughout this period," Carney continued.

Furthermore, he said, increasing the debt limit to extend the nation's borrowing authority for just another six weeks would leave the nation once again on the brink of default right around Thanksgiving and the significant holiday shopping season. "Our economy can't endure that kind of approach to resolving our budget differences."

Republicans may be willing to vote on a no-strings-attached debt limit bill now, given how poorly they've fared in a number of polls during the shutdown. The latest survey from Wall Street Journal/NBC showed 70 percent of Americans blamed congressional Republicans for putting their political agenda ahead of what's good for the country. Americans' disapproval of congressional Republicans is also at an all-time high in that poll - 53 percent - which is even higher than their negative numbers during the 1995-96 shutdown.

Reid has set up a procedural vote for Saturday on the Senate Democrats' no-strings attached debt limit bill, which would extend U.S. borrowing authority through the end of 2014. It's unclear, however, if Reid has the 60 votes necessary to advance the bill. Senate Minority Leader Mitch McConnell, R-Ky., said Thursday that Reid's proposal "just won't fly" with Republicans.

Sen. Susan Collins, R-Maine, meanwhile, has put forward a proposal that focuses on re-opening the government rather than raising the debt limit. Her plan would fund the government for six months, repeal the medical device tax (part of Obamacare) and give agencies greater flexibility to deal with across-the-board spending.

Carney said Friday, "A number of lawmakers in the Senate, as well as the House, have expressed views that are constructive in our estimation, including Sen. Collins."

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